Method for assigning a pulse response to one of a plurality of pulse types with different decay times and device for carrying out said method

ABSTRACT

A method for assigning a pulse profile, in particular a pulse profile of a scintillation detector having at least two scintillation materials with different decay characteristics, to one of a plurality of pulse types with differing decay times, encompasses the method steps of: acquiring an output pulse profile and converting the pulse profile into an electrical signal whose amplitude-time profile represents the pulse profile of the output pulse; transforming the amplitude-time profile into the frequency space in order to obtain an amplitude-frequency profile representing the output pulse; normalizing the amplitude-frequency profile in order to obtain a normalized amplitude-frequency profile; comparing the normalized amplitude-frequency profile with a predetermined reference profile; and assigning the output pulse profile to one of the pulse types on the basis of the result of the comparison.

The invention concerns a method for assigning a pulse profile, inparticular a pulse profile of a scintillation detector having at leasttwo scintillation materials with different decay characteristics, to oneof a plurality of pulse types with differing decay times. The inventionfurther concerns an apparatus for carrying out the method.

In nuclear medicine, radioactively labeled substances are used for invivo measurement of physiological processes. One sensitivenuclear-medicine method is positron emission tomography (PET). This usesisotopes that disintegrate with emission of a positron. A particularattraction of this method is the fact that some of the elements ofgreatest physiological interest, such as carbon, nitrogen, or oxygen,have short-lived radioactive isotopes that emit a positron as theydisintegrate. The emitted positron undergoes annihilation with anelectron in the tissue within a distance of 1-2 mm and generates twogamma quanta, emitted in opposite directions, with an energy of 511 keV.Simultaneous detection of the gamma quanta in oppositely locateddetectors, which are usually arranged in a detector ring, constitutesthe basis for tomographic image reconstruction.

Each detector of the ring contains a scintillation crystal that, uponimpact of a gamma quantum, emits a flash of light having a decay timethat is characteristic of the scintillation material. Bismuth germanate(BSO), for example, which is often used, has a decay time of 300 ns,which together with its relative low light yield limits the positionalresolution that can be achieved. Newer scintillation materials withgreat potential for PET applications include lutetium oxyorthosilicate(LSO) with eight times the light yield of BSO and a decay time of 40 ns,and LuAP (LuAlO₃), with a decay time of 17 ns. The light pulses of thescintillator crystals are sensed by a photodetector, typically aphotomultiplier or photodiode, that emits electrical signals suitablefor further processing.

In order to increase positional resolution, modern detectors contain twoor more different scintillation crystals that have different decay timesand are coupled to the same photodetector. By analyzing the outputsignals of the photodetectors it is possible to identify, on the basisof the different decay times, which detector crystal responded, and thusto ascertain the depth of interaction (DOI) in the detector.

An integrating amplifier is usually used, as the photodetector signalsare read out, to perform this assignment of the photodetector outputsignals to one of the scintillation crystals. A comparison of rise times(defined as the time from 10% to 90% of the maximum value) then allowsthe different detector pulses to be distinguished.

In another approach, a start value (beginning of the pulse) and a stopvalue (end of the pulse) are generated for each detector signal. Atime-to-amplitude converter then supplies an output signal having anamplitude that is proportional to the time between the start and stopvalues and can be used to discriminate the detector pulses.

All of the aforesaid differentiation and assignment methods exhibit lowreliability with noisy signals, and require a high sampling rate for thesignal pulses that are to be assigned.

It is therefore the object of the invention to describe a method of thekind cited initially that makes possible a reliable and efficient (interms of sampling rate) assignment of a pulse sequence to one of aplurality of pulse types with differing decay times.

This object is achieved, according to the present invention, by way of amethod for assigning a pulse profile, in particular a pulse profile of ascintillation detector having at least two scintillation materials withdifferent decay characteristics, to one of a plurality of pulse typeswith differing decay times, that encompasses the method steps of:

-   -   acquiring an output pulse profile and converting the pulse        profile into an electrical signal whose amplitude-time profile        represents the pulse profile of the output pulse;    -   transforming the amplitude-time profile into the frequency space        in order to obtain an amplitude-frequency profile representing        the output pulse;    -   normalizing the amplitude-frequency profile in order to obtain a        normalized amplitude-frequency profile;    -   comparing the normalized amplitude-frequency profile with a        predetermined reference profile; and    -   assigning the output pulse profile to one of the pulse types on        the basis of the result of the comparison.

The invention is thus based on the idea of performing the assignment toone of the pulse types not in the time space, but in the frequencyspace. For that purpose, the measured pulse profiles are normalizedafter being transformed, and compared with a reference profile that atthe same time represents a boundary profile between two different pulsetypes. Based on the result of that comparison, the measured pulseprofile can then be assigned to one of the pulse types. Adifferentiation between two pulse types generally requires onecomparison. If an assignment to one of more than two pulse types isperformed, several comparisons with more than one reference profile mayalso be necessary.

The comparison in the frequency space can be performed more reliably andsubstantially more effectively (lower sampling rate) than in the timespace. At the same time, efficient algorithms are available fortransforming the time profile of the measured pulse into the frequencyspace.

In a preferred embodiment of the method, the electrical signal issubjected, prior to the transformation into the frequency space, to ananalog/digital conversion with a predetermined sampling rate, in orderto obtain a discrete amplitude-time profile representing the outputpulse.

In the method according to the present invention, in the transformingstep the discrete amplitude-time profile is advantageously subjected toa discrete Fourier transform (DFT) in order to obtain a discreteamplitude-frequency profile. The discrete Fourier transform can becalculated, in particular, using a fast Fourier transform.

In the normalizing step, the amplitude-frequency profile isadvantageously referred to the amplitude at a frequency of zero; inparticular, it is useful to divide the amplitude-frequency profile bythe amplitude at a frequency of zero.

In a preferred refinement of the method according to the presentinvention, in the comparison step the difference profile between thenormalized amplitude-frequency profile and the reference profile isdetermined, the difference profile for each frequency is multiplied by apredetermined weighting factor, and the sum of those products over allfrequencies is calculated as the assignment parameter.

The assignment to one of the pulse types can be performed on the basisof the sign and/or the absolute value of the assignment parameter. Inparticular, in the case where the output pulse profile is assigned toone of two pulse types with differing decay times, the assignment can beperformed only on the basis of the sign of the assignment parameter.This allows a particularly simple decision as to the assignment of ameasured pulse to one of the pulse types.

In an embodiment of the method, the weighting factor is selected in sucha way that it has a maximum at small frequencies and decreases towardlarge frequencies. This accounts for the observation that the lowerfrequencies contribute more greatly than higher frequencies to thediscrimination of pulse types.

In the context explained above, it is preferred if the high-frequencycomponents of the electrical signal are suppressed by a lowpass filterbefore transformation into the frequency space. Disruptive aliasing ofsignals whose frequency is higher than half the sampling rate canthereby be prevented during digitization (A/DC) of the signal.

The method can be developed in particularly advantageous fashion by thefact that prior to the acquisition of pulse profiles that are to beassigned, a reference profile is determined by

-   -   acquiring calibration pulse profiles having a known assignment        to two pulse types with differing decay times, and converting        the respective pulse profiles into an electrical signal whose        amplitude-time profile represents the pulse profile of the        calibration pulse;    -   transforming the respective amplitude-time profile into the        frequency space in order to obtain an amplitude-frequency        profile representing the calibration pulse;    -   normalizing the amplitude-frequency profile in order to obtain a        normalized amplitude-frequency profile; and    -   defining a reference value for each frequency in such a way that        the amplitude values of the calibration pulses of the first        pulse type for that frequency are substantially greater than the        reference value, and the amplitude values of the calibration        pulses of the second pulse type for that frequency are        substantially less than the reference value.

In particular, the reference value for each frequency can advantageouslybe defined by the fact that an amplitude histogram is prepared for eachof the various pulse types, the intersection point of the envelopes ofthe histograms is identified, and the identified intersection point isdefined as the reference value.

It is viewed as particularly advantageous in the context explained aboveif, prior to the acquisition of pulse profiles to be assigned, theweighting factor is determined for each frequency by

-   -   determining the average magnitude of the deviation of the        amplitude values from the reference value for that frequency,        for each of the pulse types; and    -   defining a high weighting for that frequency for a large average        deviation magnitude, and a low weighting for that frequency for        a low average deviation magnitude.

An apparatus according to the present invention for carrying out themethod described encompasses

-   -   a means for acquiring an output pulse profile and a means for        converting the pulse profile into an electrical signal whose        amplitude-time profile represents the pulse profile of the        output pulse;    -   a means for transforming the amplitude-time profile into the        frequency space in order to obtain an amplitude-frequency        profile representing the output pulse;    -   a means for normalizing the amplitude-frequency profile in order        to obtain a normalized amplitude-frequency profile;    -   a means for comparing the normalized amplitude-frequency profile        with a predetermined reference profile;    -   a means for assigning the output pulse profile to one of the        pulse types on the basis of the result of the comparison, and        for outputting the assignment result;    -   a means for determining the reference profile;    -   a means for determining the weighting factors.

The respective means can, in principle, be constituted by a hardwarecomponent, such as a user-programmable logic circuit (FPGA), by softwarein a suitably equipped computer, or by firmware. The means can likewisebe implemented in a digital signal processor (DSP).

Further advantageous embodiments, features, and details of the inventionare evident from the dependent claims, the description of the exemplaryembodiment, and the drawings.

The invention will be explained in more detail below with reference toan exemplary embodiment in conjunction with the drawings. Only theelements essential for comprehension of the invention are depicted ineach case. In the drawings:

FIG. 1 is a block diagram of an apparatus for assigning a measured pulseprofile, according to an exemplary embodiment of the invention;

FIG. 2 is a plot of amplitude-time profiles for two signal pulses ofeach of two different scintillation crystals;

FIG. 3 is a plot of the amplitude-frequency profiles of the signalpulses of FIG. 2;

FIG. 4 is a plot of the normalized amplitude-frequency profiles of thesignal pulses in FIG. 2, and of a reference profile;

FIG. 5 is a plot of the difference between the normalizedamplitude-frequency profiles and the reference profile of FIG. 4;

FIG. 6 is a diagram indicating the weighting factors for the frequencycomponents of FIG. 5;

FIG. 7 is a plot of the weighted difference profiles of FIG. 5; and

FIG. 8 is a plot of the assignment parameter for a hundred output pulsesfrom two different scintillation crystals, determined in accordance withthe method according to the present invention.

An example of an application of the method according to the presentinvention to the assignment of a pulse profile to two pulse types isdescribed below in detail with reference to FIGS. 1 through 8.

The scintillation detector 10 that is used contains two differentscintillation crystal layers 12 and 14, arranged one behind another infront of a photodetector 16. In the exemplary embodiment, scintillationcrystal 12 is made of LSO (lutetium oxyorthosilicate), with a decay timeof 40 ns, and scintillation crystal 14 is made of LuYAP(Lu_(1-x)Y_(x)AlO₃), with a decay time of 17 ns.

To determine the reference profile and the weighting factors, firstlycalibration pulses having a known assignment to the fast LuYAP crystalor the slower LSO crystal were acquired. The electrical pulse profilesof the calibration pulses supplied by photodetector 16 werelowpass-filtered using a second-order Butterworth filter 22 and a limitfrequency of 10 MHz. The pulses were then digitized by A-D converter 24at a sampling rate f_(s) of 40 MHz, corresponding to twice the limitfrequency of the lowpass filter.

The result after lowpass filtering and digitization is shown in FIG. 2for two pulses each of LSO crystal 12 (reference characters 42H, 42N)and of LuYAP crystal 14 (reference characters 44H, 44N). To betterillustrate the method, one pulse with high energy (LSO: 42H; LUYAP: 44H)and one pulse with low energy (LSO: 42N; LUYAP: 44N) is selected anddepicted in each case.

The amplitude-time profiles are then inputted into assignment apparatus26, which encompasses user-programmable logic circuits 28, 30, 32, 34,and 36 whose function is evident from the description below.

The amplitude-time profiles of the calibration pulses are firstlyFourier transformed by means of a 32-point FFT (reference character 28),thereby achieving a resolution [Delta]f of 40 MHz/32=1.25 MHz at theaforesaid sampling rate.

Because the pulse shapes of the two detectors differ principally in thelower-frequency region below 10 MHz, good assignment results at the sameresolution [Delta]f=1.25 MHz would be achieved even with a lowersampling rate of f_(s)=20 MHz, a lowpass filter with a limit frequencyof 10 MHz, and a 16-point FFT. As described below in detail, theresidue, i.e., the remaining frequency region above 10 MHz using thehigher sampling rate resulted in a more reliable (97%) assignment of thepulses, but required greater calculation outlay because of the largernumber of FFT points.

The result of the 32-point FFT for the four pulse profiles of FIG. 2 isdepicted in FIG. 3. The i-th FFT component on the horizontal axiscorresponds to f_(i)=(i−1)*1.25 MHz, and the vertical axis indicates theamplitude A(f_(i)) of the pulse profiles at frequency f_(i). Because ofthe symmetry of the 32 FFT components, only the first 16 FFT componentsare shown in FIG. 3. The amplitude-frequency profiles of the fourcalibration pulses are depicted by squares 52H (LSO, high energy),circles 54H (LuYAP, high energy), asterisks 52N (LSO, low energy), andcrosses 54N (LuYAP, low energy). The difference in total energy isclearly evident from the different DC amplitudes for the i=1 component.

For normalization, the amplitude-frequency profile of each pulse isdivided by its first frequency component A(f₁) (reference character 30).The resulting normalized amplitude-frequency profiles A_(N)(f_(i)) arethen no longer dependent on the energy of the pulses.

FIG. 4 shows the normalized profiles, using reference characters 62H and62N for LSO and reference characters 64H and 64N for LuYAP. As isclearly evident from FIG. 4, the signals of the different detectors areseparated from one another in the frequency space by a gap that isparticularly distinct for the lower-frequency components f₂ through f₈.A reference profile 66 that extends in the middle of the gap between thetwo pulse types is likewise depicted in FIG. 4. As the Figure alsoshows, more than one frequency component can be used to differentiatethe two pulse types.

Reference profile 66 was obtained, for each frequency f_(i), by plottingthe amplitude values for a series of calibration pulses of each pulsetype in an amplitude histogram. The intersection point of the envelopesof the respective amplitude histograms yields the value of the referenceprofile R(f_(i)) for that frequency f_(i).

The difference between the normalized amplitude-frequency profilesA_(N)(f_(i)) and the reference profile R(f_(i)) was then calculated(reference character 32). The result is shown in FIG. 5 as 72H and 72Nfor the LSO pulses, and 74H and 74N for the LuYAP pulses. The differencevalues are for the most part positive for the LSO pulses, substantiallynegative for the LuYAP pulses. As is apparent from FIG. 5, the differentpulses can easily be separated at the lower frequency components, butdifferentiation becomes impossible for higher frequency components.

To account for this situation, for each frequency component a weightingfactor W(f_(i)) was defined, representing an indication of thesuitability of that frequency component for pulse type discrimination.The average magnitude of the deviation of the amplitude values from thereference value for each of the pulse types was taken in each case asthe indication of differentiation suitability. From the amplitudesdepicted in FIG. 5, the weighting factors W(f_(i)) shown by way ofexample in FIG. 6 can be calculated for each frequency component f_(i).As is also graphically clear from FIG. 5, the components with a lowindex, in particular the frequency components at 2.5 MHz and 3.75 MHz,receive a high weight in this context, while the weighting factors forthe higher frequencies, which do not contribute to discrimination, areset to zero.

The reference profile R(f_(i)) and weighting factors W(f_(i)) thusdetermined are stored, and can then be used, as presented below, for theassignment of measured pulse profiles whose origin from one of the twodetectors is not known.

For illustration, assignment on the basis of the previously usedcalibration pulses from the LSO and LuYAP crystals will be explained.When a new pulse of unknown 5 assignment is measured, the stepsdescribed above (with the exception of calculation of the referenceprofile and weighting factors) are therefore performed.

The difference between the normalized amplitude-frequency profileA_(N)f(_(i)) and the reference profile R(f_(i)) for each frequency isthen multiplied by the weighting factor:D _(E)(f _(i))=W(f _(i))*(A _(N)(f _(i))−R(f _(i)))to obtain a weighted difference D_(W)(f_(i)) (reference character 34).The value profiles, weighted in this fashion, are depicted in FIG. 7 as82H and 82N for the LSO pulses, and 84H and 84N for the LuYAP pulses.

Summing over the contributions of all frequencies then yields theassignment parameter Z for each pulse (reference character 34). The signof Z is sufficient for assignment. A positive value of Z results inassignment of the measured pulse as a signal from the LSO crystal, anegative value to assignment as a signal from the LuYAP crystal(reference character 36).

In order to investigate the reliability of the method according to thepresent invention, once the reference profile R(f_(i)) and weightingfactors W(f_(i)) had been defined, one hundred output pulses—fifty fromthe LSO crystal and fifty from the LuYAP crystal—were assigned inaccordance with the method explained above. FIG. 8 shows the respectiveassignment parameters Z for the LSO pulses (reference character 92) andLuYAP pulses (reference character 94). The Z values for the fourcalibration pulses are likewise plotted as 92H, 92N, 94H, and 94N. As isapparent from the Figure, the method according to the present inventionresults in correct assignment of 97% of the pulses.

1. A method for assigning a pulse profile, in particular a pulse profile of a scintillation detector having at least two scintillation materials with different decay characteristics, to one of a plurality of pulse types with differing decay times, comprising the method steps of acquiring an output pulse profile and converting the pulse profile into an electrical signal whose amplitude-time profile represents the pulse profile of the output pulse; transforming the amplitude-time profile into the frequency space in order to obtain an amplitude-frequency profile representing the output pulse; normalizing the amplitude-frequency profile in order to obtain a normalized amplitude-frequency profile; comparing the normalized amplitude-frequency profile with a predetermined reference profile; and assigning the output pulse profile to one of the pulse types on the basis of the result of the comparison.
 2. The method as defined in claim 1, wherein the electrical signal is subjected, prior to the transformation into the frequency space, to an analog/digital conversion with a predetermined sampling rate, in order to obtain a discrete amplitude-time profile representing the output pulse.
 3. The method as defined in claim 2, wherein in the transforming step, the discrete amplitude-time profile is subjected to a discrete Fourier transform (DFT) in order to obtain a discrete amplitude-frequency profile.
 4. The method as defined in claim 3, wherein the discrete Fourier transform is calculated using a fast Fourier transform (FFT).
 5. The method as defined in claim 1, wherein in the normalizing step, the amplitude-frequency profile is referred to the amplitude at a frequency of zero; in particular, the amplitude-frequency profile is divided by the amplitude at a frequency of zero.
 6. The method as defined in claim 1, wherein in the comparison step, the difference profile between the normalized amplitude-frequency profile and the reference profile is determined, the difference profile for each frequency is multiplied by a predetermined weighting factor, and the sum of those products over all frequencies is calculated as the assignment parameter.
 7. The method as defined in claim 6, wherein the assignment to one of the pulse types is performed on the basis of the sign and/or the absolute value of the assignment parameter.
 8. The method as defined in claim 6, wherein the output pulse profile is assigned to one of two pulse types with differing decay times, and the assignment is performed only on the basis of the sign of the assignment parameter.
 9. The method as defined in claim 6, wherein the weighting factor has a maximum at small frequencies and decreases toward large frequencies.
 10. The method as defined in claim 1, wherein high-frequency components of the electrical signal are suppressed by a lowpass filter before transformation into the frequency space.
 11. The method as defined in claim 1, wherein prior to the acquisition of pulse profiles that are to be assigned, a reference profile is determined by acquiring calibration pulse profiles having a known assignment to two pulse types with differing decay times, and converting the respective pulse profiles into an electrical signal whose amplitude-time profile represents the pulse profile of the calibration pulse; transforming the respective amplitude-time profile into the frequency space in order to obtain an amplitude-frequency profile representing the calibration pulse; normalizing the amplitude-frequency profile in order to obtain a normalized amplitude-frequency profile; and defining a reference value for each frequency in such a way that the amplitude values of the calibration pulses of the first pulse type for that frequency are substantially greater than the reference value, and the amplitude values of the calibration pulses of the second pulse type for that frequency are substantially less than the reference value.
 12. The method as defined in claim 11, wherein the reference value for each frequency is defined by the fact that an amplitude histogram is prepared for each of the various pulse types, the intersection point of the envelopes of the histograms is identified, and the identified intersection point is defined as the reference value.
 13. The method as defined in claim 11, wherein prior to the acquisition of pulse profiles to be assigned, the weighting factor is determined for each frequency by determining the average magnitude of the deviation of the amplitude values from the reference value for that frequency, for each of the pulse types; and defining a high weighting for that frequency for a large average deviation magnitude, and a low weighting for that frequency for a low average deviation magnitude.
 14. An apparatus for carrying out the method described as defined in claim 1, comprising a means for acquiring an output pulse profile and a means (10) for converting the pulse profile into an electrical signal whose amplitude-time profile represents the pulse profile of the output pulse; a means (28) for transforming the amplitude-time profile into the frequency space in order to obtain an amplitude-frequency profile representing the output pulse; a means (30) for normalizing the amplitude-frequency profile in order to obtain a normalized amplitude-frequency profile; a means (32, 34) for comparing the normalized amplitude-frequency profile with a predetermined reference profile; and a means (36) for assigning the output pulse profile to one of the pulse types on the basis of the result of the comparison, and for outputting the assignment result.
 15. The apparatus as defined in claim 14, in which the means (32, 34) for comparing and the means (36) for assigning are constituted by a user-programmable logic circuit (FPGA) or a digital signal processor (DSP) or (PC).
 16. The apparatus as defined in claim 15, in which the means (28) for transforming and the means (30) for normalizing are constituted by a user-programmable logic circuit (FPGA) or a digital signal processor (DSP) or (PC). 